Multi-Objective Trajectory Optimization of a Hypersonic Reconnaissance Vehicle with Temperature Constraints

Temperature-constrained optimal trajectories for a scramjet-based hypersonic reconnaissance vehicle were generated by developing an optimal control formulation and solving it using a variable order Gauss-Radau quadrature collocation method. The vehicle was assumed to be an air-breathing reconnaissance aircraft that has specified takeoff/landing locations, airborne refueling constraints, specified no-fly zones, and specified targets for sensor data collections. The aircraft model included fight dynamics, aerodynamics, and thermal constraints. This model was incorporated into an optimal control formulation that includes constraints on both the vehicle as well as mission parameters, such as avoidance of no-fly zones and coverage of high-value targets. Optimal trajectories were be developed using several different performance costs in the optimal control formulation--minimum time, minimum time with control penalties, and maximum range. The resulting analysis demonstrated that optimal trajectories that meet specified mission parameters and constraints can be determined and used for larger-scale operational and campaign planning

Optimal Ascent Guidance for Air-Breathing Launch Vehicle Based on Optimal Trajectory Correction

An optimal guidance algorithm for air-breathing launch vehicle is proposed based on optimal trajectory correction. The optimal trajectory correction problem is a nonlinear optimal feedback control problem with state inequality constraints which results in a nonlinear and nondifferentiable two-point boundary value problem (TPBVP). It is difficult to solve TPBVP on-board. To reduce the on-board calculation cost, the proposed guidance algorithm corrects the reference trajectory in every guidance cycle to satisfy the optimality condition of the optimal feedback control problem. By linearizing the optimality condition, the linear TPBVP is obtained for the optimal trajectory correction. The solution of the linear TPBVP is obtained by solving linear equations through the Simpson rule. Considering the solution of the linear TPBVP as the searching direction for the correction values, the updating step size is generated by linear search. Smooth approximation is applied to the inequality constraints for the nondifferentiable Hamiltonian. The sufficient condition for the global convergence of the algorithm is given in this paper. Finally, simulation results show the effectiveness of the proposed algorithm

Trajectory optimization using indirect methods and parametric scramjet cycle analysis

This study investigates the solution of time sensitive regional strike trajectories for hypersonic missiles. This minimum time trajectory is suspected to be best performed by scramjet powered hypersonic missiles which creates strong coupled interaction between the flight dynamics and the performance of the engine. Comprehensive engine models are necessary to gain better insight into scramjet propulsion. Separately, robust and comprehensive trajectory analysis provides references for vehicles to fly along. However, additional observation and understanding is obtained by integrating the propulsion model inside the trajectory framework. Going beyond curve fitted thrusting models, an integrated scramjet cycle analysis offers rapid trade studies on engine parameters and enables the identification of the most significant and optimal engine parameters for the mission as a whole. Regularization of bang-bang control problems by use of the Epsilon-Trig regularization method has created the possibility to preserve the original equations of motion while still solving these problems through indirect methods. Indirect methods incorporate mathematical information from the optimal control problem to provide high quality, integrated solutions. The minimum time optimal trajectory of a rocket propelled missile is compared to that of a scramjet powered missile to determine the advantages of scramjet technology in this application

상승단계 발사체의 최적 궤적 생성 및 강건 제어 기법

학위논문 (박사)-- 서울대학교 대학원 : 공과대학 기계항공공학부, 2018. 2. 김현진.This research focused on trajectory generation and control of a flexible launch vehicle during ascent flight. An important issue of a launch vehicle design is generating optimal trajectory during its atmospheric ascent flight while satisfying constraints such as aerodynamic load. These constraints become more significant due to wind disturbance, especially in the maximum dynamic pressure region. On the other hand, modern launch vehicles are becoming long and slender for the reduction in structure mass to increase payload. As a result, they possess highly flexible bending modes in addition to aerodynamically unstable rigid body characteristics. This dissertation proposes a rapid and reliable optimization approach for trajectory generation via sequential virtual motion camouflage (VMC) and non-conservative robust control for an unstable and flexible launch vehicle. First, an optimal trajectory is generated in a rapid and reliable manner through the introduction of the virtual motion camouflage. VMC uses an observed biological phenomenon called motion camouflage to construct a subspace in which the solution trajectory is generated. By the virtue of this subspace search, the overall dimension of the optimization problem is reduced, which decreases the computational time significantly compared to a traditional direct input programming. Second, an interactive optimization algorithm is proposed to find a feasible solution easier. For this, the constraint correction step is added after VMC optimization. Since VMC is a subspace problem, a feasible solution may not exist when subspace is not properly constructed. In order to address this concern, a quadratic programming (QP) problem is formulated to find a direction along which the parameters defining the subspace can be improved. Via a computationally fast QP, specific parameters (such as prey and reference point) used in VMC can be refined quickly and sequentially. As a result, the proposed interactive optimization algorithm is less sensitive to the initial guess of the optimization parameters. Third, a non-conservative 2-DOF H infty controller for an unstable and flexible launch vehicle is proposed. The objectives of the control system are to provide sufficient margins for the launch vehicle dynamics and to enhance the speed of the closed-loop response. For this, a robust control approach is used. The key of the control design is to overcome conservativeness of the robust control. The baseline controllers using the optimal control such as LQG and LQI are designed prior to a robust controller. These optimal controllers are used to find a desirable shape of the sensitivity transfer function in order to reduce conservativeness of the robust control. After implementation and analysis of the baseline controllers, an improved sensitivity weighting function is defined as a non-conventional form with different slopes in the low frequency and around crossover frequency, which results in performance enhancement without loss of robustness. A two-degree-of-freedom H infty controller is designed which uses feedback and feedforward control together to improve tracking performance with the proposed sensitivity weighting function as a target closed-loop shape. The resulting H infty controller stabilizes the unstable rigid body dynamics with sufficient margins in the low frequency, and also uses gain stabilization in addition to phase stabilization to handle the lightly damped bending modes in the high-frequency region.1 Introduction 1 1.1 Background and motivations 1 1.2 Literature survey 3 1.2.1 Optimal trajectory generation for a launch vehicle 3 1.2.2 Controller design for a flexible launch vehicle 5 1.3 Research objectives and contributions 6 1.4 Thesis organization 7 2 Launch Vehicle Dynamics 9 2.1 Frame and coordinate 9 2.2 Rigid body motion 9 2.3 Aerodynamic forces and moments 12 2.4 Gravity force 14 2.5 Thrust forces and moments 14 2.6 Flexible bending modes 15 3 Optimal Trajectory Generation 16 3.1 VMC based trajectory optimization 16 3.1.1 Nonlinear constrained trajectory optimization problem 17 3.1.2 VMC formulation 17 3.2 VMC based trajectory optimization applied to the launch vehicle 21 3.2.1 Relationship between launch vehicle dynamics and VMC 21 3.2.2 Selection of reference point and virtual prey motion 23 3.2.3 Trajectory optimization via VMC 25 3.2.4 Sequential VMC: constraint correction 27 3.2.5 Comparison study 29 3.3 Numerical simulations 31 3.3.1 Case 1: No wind disturbance 36 3.3.2 Case 2: Z-axis wind disturbance 39 3.3.3 Case 3: Y -axis wind disturbance 43 3.3.4 Case 4: Z and Y -axes wind disturbance 48 3.3.5 Performance comparison 51 4 Robust Control 57 4.1 Launch vehicle model description 57 4.1.1 Rigid body model 58 4.1.2 Flexible modes and Actuator 59 4.1.3 System properties and design specications 63 4.2 Baseline controllers design 65 4.2.1 Set-point LQG 65 4.2.2 Integral LQG 69 4.3 Robust controller design 74 4.3.1 H infinity control theory 74 4.3.2 Two-degree-of freedom H infinity controller 76 4.3.3 Selection of weighting functions: Wp and Wu 77 4.3.4 Synthesis results 82 4.3.5 Comparison study 88 4.4 Numerical simulation 94 5 Conclusions 98 Abstract (in Korean) 106Docto

Towards the Real-Time Application of Indirect Methods for Hypersonic Missions

Conceptual hypersonic mission design has typically been performed in a computationally intensive, iterative manner using direct optimization methods. The introduction of modern computing has resulted in the widespread adoption of direct methods, and useful information associated with optimal solutions has been lost. Optimization through indirect methods leverages this information, yielding high quality trajectories while reducing the dimensionality of the overall problem

Algorithmic Advances to Increase the Fidelity Of Conceptual Hypersonic Mission Design

The contributions of this dissertation increase the fidelity of conceptual hypersonic mission design through the following innovations: 1) the introduction of coupling between the effects of ablation of the thermal protection system (TPS) and flight dynamics, 2) the introduction of rigid body dynamics into trajectory design, and 3) simplifying the design of hypersonic missions that involve multiple phases of flight. These contributions are combined into a unified conceptual mission design framework, which is in turn applicable to slender hypersonic vehicles with ablative TPS. Such vehicles are employed in military applications, wherein speed and terminal energy are of critical importance. The fundamental observation that results from these contributions is the substantial reduction in the maximum terminal energy that is achievable when compared to the state-of-the art conceptual design process. Additionally, the control history that is required to follow the maximum terminal energy trajectory is also significantly altered, which will in turn bear consequence on the design of the control actuators. The other important accomplishment of this dissertation is the demonstration of the ability to solve these class of problems using indirect methods. Despite being built on a strong foundation of the calculus of variations, the state-of-the-art entirely neglects indirect methods because of the challenge associated with solving the resulting boundary value problem (BVP) in a system of differential-algebraic equations (DAEs). Instead, it employs direct methods, wherein the optimality of the calculated trajectory is not guaranteed. The ability to employ indirect methods to solve for optimal trajectories that are comprised of multiple phases of flight while also accounting for the effects of ablation of the TPS and rigid body dynamics is a substantial advancement in the state-of-the-art

Design of a hypersonic airbreathing cruise missile

In this project, a hypersonic airbreathing cruise missile is designed through an optimization process. The main use of this futuristic weapon technology is to be employed against enemy ships while being launched from an Mk-41 VLS launcher, the most widespread VLS in the world. In this optimization process and for this type of missile, Genetic Algorithms and Monte Carlo simulations are used to find an optimal solution for the rocket booster engine, the scramjet engine, aerodynamics and warhead sizing. With this data, trajectory, stability and manoeuvrability is studied to determine the performance of the missile. Other aspects concerning the missile materials of the airframe and dome are discussed on a qualitative way and no structural analysis is studied within this project. It should be noted that hypersonic weapons are mature technologies, and the only information about them are research papers regarding their aerodynamics and propulsion systems. Then, the only built hypersonic vehicles are experimental, meaning that the baseline data to start design process scarce. This brings a great challenge to this project, where creativity and the use of analytical expressions for rapid missile synthesis and conceptual design is a must. On the other side, due to the complex behaviour of hypersonic flows, this adds difficulties to our research since most of the methods employed are numerical, which can be calculated easily on a CFD in the final stages of the design, but they are not fast enough to be implemented on the initial stages of design. The final results prove that the methods employed for initial sizing are accurate enough to model a CAD design which can be used as a baseline for future research in this technology. To conclude with, the final results obtained with the algorithms helps us to understand the effects on design, especially when flying at high Mach numbers where the classical configuration of airframe, wings and tail must be radically redesigned to more aerodynamic efficient bodies such as Waveriders. Regarding to the optimization process, objective functions were changed manually to find better results at each iteration of the optimization process but better techniques such as local search methods used in artificial intelligence could be employed

Efficient Numerical Simulation of Aerothermoelastic Hypersonic Vehicles

Efficient Numerical Simulation of Aerothermoelastic Hypersonic Vehicles Hypersonic vehicles operate in a high-energy flight environment characterized by high dynamic pressures, high thermal loads, and non-equilibrium flow dynamics. This environment induces strong fluid, thermal, and structural dynamics interactions that are unique to this flight regime. If these vehicles are to be effectively designed and controlled, then a robust and intuitive understanding of each of these disciplines must be developed not only in isolation, but also when coupled. Limitations on scaling and the availability of adequate test facilities mean that physical investigation is infeasible. Ever growing computational power offers the ability to perform elaborate numerical simulations, but also has its own limitations. The state of the art in numerical simulation is either to create ever more high-fidelity physics models that do not couple well and require too much processing power to consider more than a few seconds of flight, or to use low-fidelity analytical models that can be tightly coupled and processed quickly, but do not represent realistic systems due to their simplifying assumptions. Reduced-order models offer a middle ground by distilling the dominant trends of high-fidelity training solutions into a form that can be quickly processed and more tightly coupled. This thesis presents a variably coupled, variable-fidelity, aerothermoelastic framework for the simulation and analysis of high-speed vehicle systems using analytical, reduced-order, and surrogate modeling techniques. Full launch-to-landing flights of complete vehicles are considered and used to define flight envelopes with aeroelastic, aerothermal, and thermoelastic limits, tune in-the-loop flight controllers, and inform future design considerations. A partitioned approach to vehicle simulation is considered in which regions dominated by particular combinations of processes are made separate from the overall solution and simulated by a specialized set of models to improve overall processing speed and overall solution fidelity. A number of enhancements to this framework are made through 1. the implementation of a publish-subscribe code architecture for rapid prototyping of physics and process models. 2. the implementation of a selection of linearization and model identification methods including high-order pseudo-time forward difference, complex-step, and direct identification from ordinary differential equation inspection. 3. improvements to the aeroheating and thermal models with non-equilibrium gas dynamics and generalized temperature dependent material thermal properties. A variety of model reduction and surrogate model techniques are applied to a representative hypersonic vehicle on a terminal trajectory to enable complete aerothermoelastic flight simulations. Multiple terminal trajectories of various starting altitudes and Mach numbers are optimized to maximize final kinetic energy of the vehicle upon reaching the surface. Surrogate models are compared to represent the variation of material thermal properties with temperature. A new method is developed and shown to be both accurate and computationally efficient. While the numerically efficient simulation of high-speed vehicles is developed within the presented framework, the goal of real time simulation is hampered by the necessity of multiple nested convergence loops. An alternative all-in-one surrogate model method is developed based on singular-value decomposition and regression that is near real time. Finally, the aeroelastic stability of pressurized cylindrical shells is investigated in the context of a maneuvering axisymmetric high-speed vehicle. Moderate internal pressurization is numerically shown to decrease stability, as showed experimentally in the literature, yet not well reproduced analytically. Insights are drawn from time simulation results and used to inform approaches for future vehicle model development.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/138502/1/rjklock_1.pd